These stress measures refer force or area to the reference configuration. Different index-order conventions distinguish a first Piola-Kirchhoff stress tensor from its transposed nominal stress tensor. The second Piola-Kirchhoff stress tensor has two material indices.
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The Piola-Kirchhoff stress tensors are mathematical constructs used in the field of continuum mechanics to describe the state of stress in a deformable body. They provide a way to relate the stresses in a material to its deformation, capturing both the current configuration and the reference (or undeformed) configuration of the material.